“Holography” has been known as a three-dimensional image display technique. Holography is a technique of reconstructing the optical wavefront of object light coming from an object as a three-dimensional image by irradiating illuminating light onto a display device on which a control image (an interference pattern of light in which phase or amplitude is controlled) is recorded
There is a known holographic method in which a “kinoform” constituted by the phase distribution of an optical wavefront for modulating the phase of irradiated light is used. This method supposes that in a control image recorded on a display device, the amplitude of the optical wavefront is constant and only the phase of the optical wavefront is distributed.
In such a method, there is a known way using a “Simulated Annealing” method of determining the phase distribution of an optical wavefront optimum for reconstructing a three-dimensional image.
The “Simulated Annealing” method is a stochastic search method of obtaining an optimum solution by repeating an operation of changing a solution to another solution (Move operation), and searching a solution space.
In the “Simulated Annealing” method, when solution evaluation is elevated by a Move operation (that is, a solution is improved), the solution change by the Move operation is accepted.
On the other hand, in the “Simulated Annealing” method, when change by a Move operation worsens solution evaluation (that is, a solution is worsened), it is determined whether to accept the solution change by the Move operation or not (that is, whether to return the solution after the Move operation to the solution before the Move operation or not) based on the acceptance probability P (=exp(−ΔE/T)) which is calculated based on a parameter T representing “temperature” (hereinafter, temperature parameter T) and a worsened amount of ΔE.
Here, by gradually decreasing the temperature parameter T from a sufficiently high temperature after the start of experiment to a sufficiently low temperature, and controlling the above-described acceptance probability P, computation of local optimum solutions can be prevented.
In the above method, a comparison is made between an image to be reconstructed given as an input (hereinafter,input image) and a reconstructed image obtained by Fourier transforming the phase distribution of an optical wavefront on a kinoform, to evaluate solutions before and after a Move operation.
Since the calculation amount In the solution evaluation process is vast, a technique has been proposed in which solution evaluation is performed based on difference information about reconstructed images before and after a Move operation to shorten time for searching for an optimum solution in the “Simulated Annealing” method.
As described above, in the conventional three-dimensional image display technique, solution evaluation was performed based on difference information about reconstructed images before and after a Move operation to shorten time for searching for an optimum solution in the “Simulated Annealing” method.
However, the conventional three-dimensional image display technology has had the problem that since a control image obtained by Fourier transforming an input image is used as an initial solution in the “Simulated Annealing” method, when the fast Fourier transformation algorithm is used, a calculation amount of “O(NlogN)” where “N=(Nx×Ny)” is the size of the input image (kinoform) is required for evaluating the initial solution, making it impossible to shorten much time for searching for an optimum solution.
The calculation amount of “O(NlogN)” means the complexity of the calculation is the order of NlogN.
Also, the conventional three-dimensional image display technique has had the problem that even though change of one point on a kinoform does not necessarily have an effect on every point of a reconstructed image due to the characteristics of a display device on which the kinoform is recorded, calculation s performed on the assumption that change of one point on the kinoform has an effect on every point of the reconstructed image, and thus, while the calculation amount in a solution evaluation after a Move operation can be reduced from the calculation amount “O(NlogN)” required for normal Fourier transformation to “O(N),” redundant calculation is still performed.
The present invention has been made in view of the above problems, and has an object of providing three-dimensional image display devices and three-dimensional image display methods which allow a reduction in redundant calculation and high-speed obtainment of an optimum control image to be recorded on a display device.